4747``` python
4848class Solution :
4949 def multiply (self num1 : str , num2 : str ) -> str :
50- def add (s1 , s2 ):
51- n1, n2 = len (s1), len (s2)
52- i = carry = 0
53- res = []
54- while i < max (n1, n2) or carry > 0 :
55- a = int (s1[n1 - i - 1 ]) if i < n1 else 0
56- b = int (s2[n2 - i - 1 ]) if i < n2 else 0
57- carry, t = divmod (a + b + carry, 10 )
58- res.append(str (t))
59- i += 1
60- return ' ' - 1 ])
61-
62- if ' 0' in [num1, num2]:
63- return ' 0'
64- n1, n2 = len (num1), len (num2)
65- ans = ' '
66- for i in range (n1):
67- a = int (num1[n1 - i - 1 ])
68- t = ' '
69- for j in range (n2):
70- b = int (num2[n2 - j - 1 ])
71- t = add(t, str (a * b) + ' 0' * j)
72- ans = add(ans, t + ' 0' * i)
73- return ans
50+ def mul (b , i ):
51+ j, t = m - 1 , 0
52+ while j >= 0 or t:
53+ if j >= 0 :
54+ a = int (num1[j])
55+ t += a * b
56+ res[i] += t % 10
57+ if res[i] >= 10 :
58+ res[i] %= 10
59+ res[i + 1 ] += 1
60+ i, j = i + 1 , j - 1
61+ t //= 10
62+
63+ m, n = len (num1), len (num2)
64+ res = [0 ] * (m + n)
65+ for i in range (n):
66+ b = int (num2[n - 1 - i])
67+ mul(b, i)
68+ while len (res) > 1 and res[- 1 ] == 0 :
69+ res.pop()
70+ return ' ' str (v) for v in res[::- 1 ]])
7471```
7572
7673### ** Java**
@@ -80,43 +77,114 @@ class Solution:
8077``` java
8178class Solution {
8279 public String multiply (String num1 , String num2 ) {
83- if (Objects . equals(num1, " 0" || Objects . equals(num2, " 0"
84- return " 0"
80+ int m = num1. length(), n = num2. length();
81+ int [] res = new int [m + n];
82+ for (int i = 0 ; i < n; ++ i) {
83+ int b = num2. charAt(n - 1 - i) - ' 0'
84+ mul(num1, b, i, res);
8585 }
86- int n1 = num1. length(), n2 = num2. length();
87- String ans = " "
88- for (int i = 0 ; i < n1; ++ i) {
89- int a = num1. charAt(n1 - i - 1 ) - ' 0'
90- String t = " "
91- for (int j = 0 ; j < n2; ++ j) {
92- int b = num2. charAt(n2 - j - 1 ) - ' 0'
93- StringBuilder sb = new StringBuilder (String . valueOf(a * b));
94- for (int k = 0 ; k < j; ++ k) {
95- sb. append(0 );
96- }
97- t = add(t, sb. toString());
86+ StringBuilder ans = new StringBuilder ();
87+ for (int v : res) {
88+ ans. append(v);
89+ }
90+ while (ans. length() > 1 && ans. charAt(ans. length() - 1 ) == ' 0'
91+ ans. deleteCharAt(ans. length() - 1 );
92+ }
93+ return ans. reverse(). toString();
94+ }
95+
96+ private void mul (String A , int b , int i , int [] res ) {
97+ for (int j = A . length() - 1 , t = 0 ; j >= 0 || t > 0 ; -- j) {
98+ if (j >= 0 ) {
99+ int a = A . charAt(j) - ' 0'
100+ t += a * b;
98101 }
99- StringBuilder sb = new StringBuilder (t);
100- for (int k = 0 ; k < i; ++ k) {
101- sb. append(0 );
102+ res[i++ ] += t % 10 ;
103+ if (res[i - 1 ] >= 10 ) {
104+ res[i - 1 ] %= 10 ;
105+ ++ res[i];
102106 }
103- ans = add(ans, sb. toString());
107+ t /= 10 ;
108+ }
109+ }
110+ }
111+ ```
112+
113+ ### ** C++**
114+
115+ ``` cpp
116+ class Solution {
117+ public:
118+ string multiply(string num1, string num2) {
119+ int m = num1.size(), n = num2.size();
120+ vector<int > res(m + n);
121+ for (int i = 0; i < n; ++i)
122+ {
123+ int b = num2[ n - 1 - i] - '0';
124+ mul(num1, b, i, res);
104125 }
126+ string ans = "";
127+ for (int v : res) ans.push_back(v + '0');
128+ while (ans.size() > 1 && ans.back() == '0') ans.pop_back();
129+ reverse(ans.begin(), ans.end());
105130 return ans;
106131 }
107132
108- private String add (String s1 , String s2 ) {
109- int n1 = s1. length(), n2 = s2. length();
110- StringBuilder res = new StringBuilder ();
111- for (int i = 0 , carry = 0 ; i < Math . max(n1, n2) || carry > 0 ; ++ i) {
112- int a = i < n1 ? (s1. charAt(n1 - i - 1 ) - ' 0' : 0 ;
113- int b = i < n2 ? (s2. charAt(n2 - i - 1 ) - ' 0' : 0 ;
114- int s = a + b + carry;
115- carry = s / 10 ;
116- res. append(s % 10 );
133+ void mul(string A, int b, int i, vector<int>& res) {
134+ for (int j = A.size() - 1, t = 0; j >= 0 || t > 0; --j)
135+ {
136+ if (j >= 0)
137+ {
138+ int a = A[j] - '0';
139+ t += a * b;
140+ }
141+ res[i++] += t % 10 ;
142+ if (res[i - 1 ] >= 10 )
143+ {
144+ res[i - 1] %= 10;
145+ ++res[i];
146+ }
147+ t /= 10;
117148 }
118- return res. reverse(). toString();
119149 }
150+ };
151+ ```
152+
153+ ### ** Go**
154+
155+ ``` go
156+ func multiply (num1 string , num2 string ) string {
157+ m , n := len (num1), len (num2)
158+ res := make ([]int , m+n)
159+ mul := func (b, i int ) {
160+ for j , t := m-1 , 0 ; j >= 0 || t > 0 ; i, j = i+1 , j-1 {
161+ if j >= 0 {
162+ a := int (num1[j] - ' 0'
163+ t += a * b
164+ }
165+ res[i] += t % 10
166+ if res[i] >= 10 {
167+ res[i] %= 10
168+ res[i+1 ]++
169+ }
170+ t /= 10
171+ }
172+ }
173+ for i := 0 ; i < n; i++ {
174+ b := num2[n-1 -i] - ' 0'
175+ mul (int (b), i)
176+ }
177+ var ans []byte
178+ for _ , v := range res {
179+ ans = append (ans, byte (v+' 0'
180+ }
181+ for len (ans) > 1 && ans[len (ans)-1 ] == ' 0'
182+ ans = ans[:len (ans)-1 ]
183+ }
184+ for i , j := 0 , len (ans)-1 ; i < j; i, j = i+1 , j-1 {
185+ ans[i], ans[j] = ans[j], ans[i]
186+ }
187+ return string (ans)
120188}
121189```
122190
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